1. Field of the Invention
The present invention relates generally to processing methods for adaptive filtering on a source signal for transmission, and more particularly an adaptive filtering method to identify the relationship between a source signal and a received signal.
2. Description of the Related Art
It will be readily appreciated by one skilled in the art that the use of adaptive filtering operations may be required in a variety of different signal processing applications. One example of such an area is that of acoustics and specifically sonar signaling. Adaptive filtering systems for time varying operators have broad applications. For example, echo cancellation, active and passive sonar, and equalization of communication signals employ adaptive filtering modeling regimes for extracting information from signals. These modeling regimes are often limited by available memory, computational resources, and acceptable processing delays.
Multiresolution models of time varying operators have been promoted with the idea of exploiting the sparsity or “economy” of representation attendant in them. This is a useful concept since many operators that are not shift invariant are often succinctly described in wavelet bases, the basic building block of multiresolution models. Conventional approaches have given a general framework for formulating the multiresolution filter structures and provided a fast least mean square-like estimators with an assumed maximal scale of representation. However, this assumption is often overly optimistic. In which case the maximal scale of representation or the most economical wavelet bases can be jointly estimated.
With regards to adaptive filtering, multiresolution models naturally allow estimation of the response at a given time instant based on given data. In addition, the model circumvents the need for locally stationary assumptions of time recursive algorithms. Accordingly, a larger amount of information is available for the estimation problem at each time instant. Unlike in-time estimation algorithms that are by their very nature causal or near causal, dependencies across time in the forward looking direction are not accounted for with classic in-time adaptive filtering algorithms. In-time estimation is a powerful paradigm due to its computational efficiencies and memory requirements and it continues to find broad appeal and enjoys superior performance in a variety of applications. Nevertheless in areas where fading and multipath delay do not conform to the wide sense stationary (WSS) assumption the multiresolution model is a viable solution. Other practical considerations related to using multiresolution modeling include signal processing and communication schemes involving strategies based on finite duration signaling. For example, mobile radio and underwater acoustic communications data employ a sequence of finite duration packets to transmit information. Similarly for underwater target localization by active sonar as well as radar applications source signals employ time localized “pings.”
Accordingly, a need exists for a scale adaptive filtering method that is able to match a received signal based on information from a source signal by estimating a variety of parameters. A channel operator is built up in scale, and the channel operator employs time delays and frequency spreads. For this purpose, each additional incrementation of the Doppler spread is hypothesized and then tested.